Generally, they accept photocopy, there might be exceptions.
Anyway, receipt is required only if the front-desk is stringent or trying to make things difficult for you. Else, warranty card is fine.
I have yet to encounter one which requires me to produce my receipt, throughout maybe 7 different products that I've sent for servicing or repair.
Had an Acer PC warranty, photocopied just in case.
Then my dog peed on my original warranty.:bsmilie:
Had to send PC for repair, showed photocopied version, good thing they accepted it.
Or else they'd have to face and smell the wrath of that original one.
Serial number is reflected on warranty card as a reference to compare with, the actual product.
I guess if Sigma warranty card does not state receipt is needed, then there's no need for it then. But quite often, they have a clause stating that they have the right to reject your warranty card and/or repairing your item as they see fit. Do read carefully.
Nowadays, most camera manufacturers have already wised up to this "unfilled warranty" thing that many people have been pulling off for years. Last time Konica-Minolta don't need receipt, but when Sony took over, they really implemented all kinds of safeguards to ensure this kind of thing doesn't happen.
So yes, in probably 90% of the cases, you will need a receipt to accompay the w'ty card. (But in the case of Nikon, if you lose your receipt, don't worry, they can track down where and when you bought your camera from - personal experience.)